The ever increasing demand for digital communications coupled with the fixed bandwidth available for such transmissions has increased the desirability of providing digital modulation techniques requiring a minimum bandwidth for a given bit error rate.
Perhaps the most commonly used digital modulation technique to date has been QPSK (Quaternary Phase Shift Keying). According to this technique, an incoming serial digital bit stream is divided into two separate bit streams which are used to modulate in-phase and quadrature components of a carrier signal. The modulated in-phase and quadrature components of the carrier are then summed together to produce the output QPSK signal. For certain bit combinations in the incoming bit stream, the output QPSK signal can have phase transitions of as much as 180 degrees. This gives rise to a problem of adjacent channel interference.
Specifically, in order to comply with spectrum requirements, an output QPSK signal must be band limited with a bandpass filter. The band limited QPSK signal does not have a constant envelope. In fact, the envelope can go to zero due to the 180 degree phase transitions. In a satellite repeater, the received QPSK signal must be hard limited to restore the constant envelope. Unfortunately the restoration of the constant envelope also restores the sidelobes of the QPSK signal which were removed by the bandpass filtering at the transmitter side. These sidelobes produce interference in adjacent channels.
In an attempt to at least partially overcome these disadvantages of QPSK, a technique known as OQPSK (Offset Quarternary Phase Shift Keying) has been developed. According to this technique, the incoming serial bit stream is divided into two channels, the same as QPSK. However, unlike QPSK in which the two separated bit streams are aligned at bit transition times, the two separated bit streams in OQPSK are phase shifted by 180 degrees relative to one another. By doing so, the maximum phase transition which can occur in the output OQPSK signal is limited to 90 degrees. When an OQPSK signal is utilized in a communication system as described, the effects of band limiting in the transmitter and hard limiting at the repeater produce less adjacent channel interference than with QPSK. Nonetheless, the amount of adjacent channel interference is still significant and unacceptable for some applications. Thus, it is desirable to further reduce the adverse effects of regenerated sidebands caused by discontinuities in the phase of a transmitted signal.
This has been done with a technique known as MSK (Minimum Shift Keying). This technique may be viewed as an adaptation of OQPSK modulation wherein, instead of using rectangular pulse weighting as is the case of OQPSK, sinusoidal weighting is employed. This technique is described in an article entitled "Minimum Shift Keying: A Spectrally Efficient Modulation", IEEE Communications Magazine, July 1979, by S. Pasupathy. An example of this technique will be discussed with reference to FIGS. 1, 2 and 3a-3f. It is assumed that the bit sequence which it is desired to be transmitted is +1, +1, -1, -1, -1, +1, +1, +1. This bit stream is divided into two bit streams which are modulated with signals of cos (.pi.t/2T) and sin (.pi.t/2T), respectively. The resultant signals are shown in FIGS. 3a and 3c. In the indicated waveforms, a.sub.I (t) and a.sub.Q (t) represent the respective separated bit streams. These signals are then used to modulate respective carriers in the form of cos 2.pi.f.sub.c t and sin 2.pi.f.sub.c t, where f.sub.c is the carrier signal frequency. The resulting waveforms are shown in FIGS. 3b and 3d. The signals of FIGS. 3b and 3d are summed to produce the output waveform s(t) as shown in FIG. 3e.
FIG. 3f is a phase transition diagram corresponding to the signal of FIG. 3e. From this diagram, it may readily be seen that there are no discontinuous phase transitions in the output signal produced by the MSK technique. Due to the elimination of discontinuous phase transitions, the output spectral density of MSK has lower sidelobes than either QPSK or OQPSK. This is illustrated in FIG. 1 which is a spectral density diagram comparing the two techniques.
Another way of viewing MSK is to consider it as a special case of FSK (Frequency Shift Keying). It may be demonstrated mathematically that an MSK signal is equivalent to an FSK signal with signalling frequencies of f.sub.c +(1/4)T and f.sub.c -(1/4)T, that is, a frequency deviation of .DELTA.f=(1/2)T. Because this is the minimum frequency spacing which permits two FSK signals to be coherently orthogonal, the term "minimum shift" keying is applied.
A typical prior art modulator for MSK is shown in the block diagram of FIG. 2. In this modulator, the mixer or multiplier 20 produces two phase coherent signals at frequencies of f.sub.c +(1/4)T and f.sub.c -(1/4)T. These are filtered by upper and lower frequency bandpass filters 22 and 24 to produce signals of the form: EQU s.sub.1 (t)=(1/2) cos (2.pi.f.sub.c t+.pi.(t/2)T)
and EQU s.sub.2 (t)=(1/2) cos (2.pi.f.sub.c t-.pi.(t/2)T).
The sum and difference of the signals s.sub.1 (t) and s.sub.2 (t) are formed by the adder 26 and subtractor 28. The resultant signals x(t) and y(t) are fed to multipliers 30 and 32 where they are modulated with the signals a.sub.I (t) and a.sub.Q (t).
Although MSK would appear to have some direct advantages due to its inherent improved spectral properties, direct generation of an MSK waveform utilizing a modulator such as that shown in FIG. 2 is both difficult and expensive. The multipliers required are expensive and the timing requirements quite tight. Numerous timing adjustments are necessary and the frequency deviation of 0.5T implies difficult, and perhaps impossible in some situations, filtering requirements. For these reasons, MSK modulation has not been widely used.